Bivariate Continuous Negatively Correlated Proportional Models with Applications in Schizophrenia Research

Yuan Sun, Guoliang Tian, Shuixia Guo, Lianjie Shu and Chi Zhang
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Yuan Sun: Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Guoliang Tian: Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen 518055, China
Shuixia Guo: MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China
Lianjie Shu: Faculty of Business, University of Macau, Macau, China
Chi Zhang: College of Economics, Shenzhen University, Shenzhen 518055, China

Mathematics, 2022, vol. 10, issue 3, 1-22

Abstract: Bivariate continuous negatively correlated proportional data defined in the unit square ( 0 , 1 ) 2 often appear in many different disciplines, such as medical studies, clinical trials and so on. To model this type of data, the paper proposes two new bivariate continuous distributions (i.e., negatively correlated proportional inverse Gaussian (NPIG) and negatively correlated proportional gamma (NPGA) distributions) for the first time and provides corresponding distributional properties. Two mean regression models are further developed for data with covariates. The normalized expectation–maximization (N-EM) algorithm and the gradient descent algorithm are combined to obtain the maximum likelihood estimates of parameters of interest. Simulations studies are conducted, and a data set of cortical thickness for schizophrenia is used to illustrate the proposed methods. According to our analysis between patients and controls of cortical thickness in typical mutual inhibitory brain regions, we verified the compensatory of cortical thickness in patients with schizophrenia and found its negative correlation with age.

Keywords: bivariate NPGA models; bivariate NPIG models; cortical thickness; N-EM algorithm; proportional data (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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